3, Variation on 9.4#5, #17] For the relation R represented by this directed grap

Question

3, Variation on 9.4#5, #17] For the relation R represented by this directed graph. Write the matrix representing: (a) The relation R5 points] (b) The complement of R [5 points] (c) The symmetric closure of R (d) The transitive closure of R10 points] Replace this text with your answer Replace this text with your answer Replace this text with your answer 5 points] Replace this text with your answer (e) Write all of the paths of length 2.5 points] Replace this text with your answer (f) Write all of the circuits of length 3. 5 points] Replace this text with your answer (g) Write all of the circuits of length 3 in the transitive closure of R. 10 points] Replace this text with your answer

Explanation / Answer

we are having set of four vertexes V={A, B, C, D}

Here we get R'={(B,B),(C,C),(D,D),(A,C),(A,D),(C,A),(C,B),(C,D),(D,B),(D,C)}

3.Symmetric closure of Relation: to find Symmetric closure of relation R we add edge a to b when there is already egde from b to a.

Here R = {(A,A),(A,B)(B,A),(B,C),(B,D),(D,A)}

RS= {(A,A),(A,B)(B,A),(B,C),(B,D),(D,A),(C,B),(D,B),(A,D)}

4.Transitive closure of Relation: to find Transitive closure of relation R we add edge a to c when there is already edge from a to b and b to a.

Here R = {(A,A),(A,B)(B,A),(B,C),(B,D),(D,A)}

RT={(A,A),(A,B)(B,A),(B,C),(B,D),(D,A),(A,C)}

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